{"paper":{"title":"Chaos in convolution operators on the space of entire functions of infinitely many complex variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Blas M. Caraballo, Vin\\'icius V. F\\'avaro","submitted_at":"2018-06-19T18:20:28Z","abstract_excerpt":"A classical result of Godefroy and Shapiro states that every nontrivial convolution operator on the space $\\mathcal{H}(\\mathbb{C}^n)$ of entire functions of several complex variables is hypercyclic. In sharp contrast with this result F\\'avaro and Mujica show that no translation operator on the space $\\mathcal{H}(\\mathbb{C}^\\mathbb{N})$ of entire functions of infinitely many complex variables is hypercyclic. In this work we study the linear dynamics of convolution operators on $\\mathcal{H}(\\mathbb{C}^\\mathbb{N})$. First we show that no convolution operator on $\\mathcal{H}(\\mathbb{C}^\\mathbb{N})"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07413","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}